How to train for own dataset really really fast while debugging
Assuming that you are using DarkFlow, you can train your model with --train flag and don't use --gpu flag since you don't want to use the GPU memory. And yes it's possible to train with just 10 images (basically over-fitting) just to confirm the working of your model. Place those 10 images in train/images directory and the annotations of these images in train/annotations directory (in PASCAL VOC format). 
For faster performance, use pre-trained weights file for tuning your model so that you don't need to train for initial same layers (and since you just want to detect a single object - license plates - use tiny-yolo-voc.weights.
Further more, use --epoch flag to reduce the number of epochs.

flow --model cfg/tiny-yolo-voc-new.cfg --load bin/tiny-yolo-voc.weights --train --annotation train/Annotations --dataset train/Images --epoch 20
Change the number of classes and the number of filters as defined in the readme first. Then you can change the height and width of the input image the model will be trained on. Higher resolution for more accuracy while lower resolution for higher performance and speed. You can also change the activation functions for the layers, but I recommend leaving them unchanged.